Search results for "Poisson proce"
showing 10 items of 24 documents
Modeling Energy Demand Aggregators for Residential Consumers
2013
International audience; Energy demand aggregators are new actors in the energy scenario: they gather a group of energy consumers and implement a demand- response paradigm. When the energy provider needs to reduce the current energy demand on the grid, it can pay the energy demand aggregator to reduce the load by turning off some of its consumers loads or postponing their activation. Currently this operation involves only greedy energy consumers like industrial plants. In this paper we want to study the potential of aggregating a large number of small energy consumers like home users as it may happen in smart grids. In particular we want to address the feasibility of such approach by conside…
A Criterium for the Strict Positivity of the Density of the Law of a Poisson Process
2011
We translate in semigroup theory our result (Leandre, 1990) giving a necessary condition so that the law of a Markov process with jumps could have a strictly positive density. This result express, that we have to jump in a finite number of jumps in a "submersive" way from the starting point to the end point if the density of the jump process is strictly positive in . We use the Malliavin Calculus of Bismut type of (Leandre, (2008;2010)) translated in semi-group theory as a tool, and the interpretation in semi-group theory of some classical results of the stochastic analysis for Poisson process as, for instance, the formula giving the law of a compound Poisson process.
Itô calculus extended to systems driven by -stable Lévy white noises (a novel clip on the tails of Lévy motion)
2007
Abstract The paper deals with probabilistic characterization of the response of non-linear systems under α -stable Levy white noise input. It is shown that, by properly selecting a clip in the probability density function of the input, the moments of the increments of Levy motion process remain all of the same order ( d t ) , like the increments of the Compound Poisson process. It follows that the Ito calculus extended to Poissonian input, may also be used for α -stable Levy white noise input processes. It is also shown that, when the clip on the tails of the probability of the increments of the Levy motion approaches to infinity, the Einstein–Smoluchowsky equation is restored. Once these c…
ELECTRE III to dynamically support the decision maker about the periodic replacements configurations for a multi-component system
2013
The problem tackled by the present paper concerns the selection of the elements of a repairable and stochastically deteriorating multi-component system to replace (replacements configuration) during each scheduled and periodical system stop within a finite optimization cycle, by ensuring the simultaneous minimization of both the expected total maintenance cost and the system unavailability. To solve the considered problem, a combined approach between multi-objective optimization problem (MOOP) and multi-criteria decision making (MCDM) resolution techniques is proposed. In particular, the @e constraint method is used to single out the optimal Pareto frontier whereas the ELECTRE III multi-cri…
A critical empirical study of three electricity spot price models
2012
We conduct an empirical analysis of three recently proposed and widely used models for electricity spot price process. The first model, called the jump-diffusion model, was proposed by Cartea and Figueroa (2005), and is a one-factor mean-reversion jump-diffusion model, adjusted to incorporate the most important characteristics of electricity prices. The second model, called the threshold model, was proposed by Roncoroni (2002) and further developed by Geman and Roncoroni (2006), and is an exponential Ornstein–Uhlenbeck process driven by a Brownian motion and a state-dependent compound Poisson process. It is designed to capture both statistical and pathwise properties of electricity spot pri…
A Multi-Objective Approach to Optimize a Periodic Maintenance Policy
2012
The present paper proposes a multi-objective approach to find out an optimal periodic maintenance policy for a repairable and stochastically deteriorating multi-component system over a finite time horizon. The tackled problem concerns the determination of the system elements to replace at each scheduled and periodical system inspection by ensuring the simultaneous minimization of both the expected total maintenance cost and the expected global system unavailability time. It is assumed that in the case of system elements failure they are instantaneously detected and repaired by means of minimal repair actions in order to rapidly restore the system. A nonlinear integer mathematical programmi…
Catastrophic risks and the pricing of catastrophe equity put options
2021
In this paper, after a review of the most common financial strategies and products that insurance companies use to hedge catastrophic risks, we study an option pricing model based on processes with jumps where the catastrophic event is captured by a compound Poisson process with negative jumps. Given the importance that catastrophe equity put options (CatEPuts) have in this context, we introduce a pricing approach that provides not only a theoretical contribution whose applicability remains confined to purely numerical examples and experiments, but which can be implemented starting from real data and applied to the evaluation of real CatEPuts. We propose a calibration framework based on his…
Efficient solution of the first passage problem by Path Integration for normal and Poissonian white noise
2015
Abstract In this paper the first passage problem is examined for linear and nonlinear systems driven by Poissonian and normal white noise input. The problem is handled step-by-step accounting for the Markov properties of the response process and then by Chapman–Kolmogorov equation. The final formulation consists just of a sequence of matrix–vector multiplications giving the reliability density function at any time instant. Comparison with Monte Carlo simulation reveals the excellent accuracy of the proposed method.
Poisson white noise parametric input and response by using complex fractional moments
2014
Abstract In this paper the solution of the generalization of the Kolmogorov–Feller equation to the case of parametric input is treated. The solution is obtained by using complex Mellin transform and complex fractional moments. Applying an invertible nonlinear transformation, it is possible to convert the original system into an artificial one driven by an external Poisson white noise process. Then, the problem of finding the evolution of the probability density function (PDF) for nonlinear systems driven by parametric non-normal white noise process may be addressed in determining the PDF evolution of a corresponding artificial system with external type of loading.
SOME RELATIONS BETWEEN BOUNDED BELOW ELLIPTIC OPERATORS AND STOCHASTIC ANALYSIS
2019
International audience; We apply Malliavin Calculus tools to the case of a bounded below elliptic rightinvariant Pseudodifferential operators on a Lie group. We give examples of bounded below pseudodifferential elliptic operators on R d by using the theory of Poisson process and the Garding inequality. In the two cases, there is no stochastic processes besides because the considered semi-groups do not preserve positivity.